函数y=2sin(π/4-3x)的单调递减区间是 希望能给个正确的完整答案

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函数y=2sin(π/4-3x)的单调递减区间是希望能给个正确的完整答案函数y=2sin(π/4-3x)的单调递减区间是希望能给个正确的完整答案函数y=2sin(π/4-3x)的单调递减区间是希望能给

函数y=2sin(π/4-3x)的单调递减区间是 希望能给个正确的完整答案
函数y=2sin(π/4-3x)的单调递减区间是 希望能给个正确的完整答案

函数y=2sin(π/4-3x)的单调递减区间是 希望能给个正确的完整答案
y = 2sin(π/4 - 3x) = -2sin(3x - π/4)
求减区间就是求sin(3x - π/4)的增区间
则3x - π/4 ∈(-π/2 + 2kπ,π/2 + 2kπ),k ∈Z
x ∈(-π/12 + 2kπ/3,π/4 + 2kπ/3),k ∈Z

sinx的单调区间为:[2kπ-π/2;2kπ+π/2]
所以,
y=2sin(π/4-3x)的单调递减区间是:
2kπ+π/2≤π/4-3x≤2kπ+3π/2
2kπ+π/4≤-3x≤2kπ+5π/4
-2kπ-5π/4≤3x≤-2kπ-π/4
(-2/3)kπ-5π/12≤x≤(-2/3)kπ-π/12;k∈Z两边的负号要去掉吗?楼上的回答和书上...

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sinx的单调区间为:[2kπ-π/2;2kπ+π/2]
所以,
y=2sin(π/4-3x)的单调递减区间是:
2kπ+π/2≤π/4-3x≤2kπ+3π/2
2kπ+π/4≤-3x≤2kπ+5π/4
-2kπ-5π/4≤3x≤-2kπ-π/4
(-2/3)kπ-5π/12≤x≤(-2/3)kπ-π/12;k∈Z

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单调递减区间为:[(-2/3)kπ-π/12,(-2/3)kπ+π/4](k∈Z )